dynamicwave

dynamicwave

Dynamic Wave equation

ResultQ = dynamicwaveq(Ldd, Qin, Hin,
                       ChannelBottomLevel, ChannelRoughness,
                       ChannelLength, ChannelBottomWidth,
                       ChannelDepth, ChannelForm,
                       FloodplainWidth,
                       TimeStepInSeconds, NrOfTimeSlices,
                       Structures, StructureA, StructureB, StructureCrestLevel)

ResultH = dynamicwaveh(Ldd, Qin, Hin,
                       ChannelBottomLevel, ChannelRoughness,
                       ChannelLength, ChannelBottomWidth,
                       ChannelDepth, ChannelForm,
                       FloodplainWidth,
                       TimeStepInSeconds, NrOfTimeSlices,
                       Structures, StructureA, StructureB, StructureCrestLevel)

ResultH,ResultQ = dynamicwaveq, dynamicwaveh(Ldd, Qin, Hin,
                       ChannelBottomLevel, ChannelRoughness,
                       ChannelLength, ChannelBottomWidth,
                       ChannelDepth, ChannelForm,
                       FloodplainWidth,
                       TimeStepInSeconds, NrOfTimeSlices,
                       Structures, StructureA, StructureB, StructureCrestLevel)

Argument

Type

[Units] Remarks

Ldd

ldd, spatial

Channel network

Qin

scalar, spatial

[m3/timestep] lateral inflow into the channel

Hin

scalar, spatial

[m] >= 0, water surface level at begin of timestep

ChannelBottomLevel

scalar, spatial

[m]

ChannelRoughness

scalar, spatial

[-] > 0, if manning: Manning coefficient

if chezy: Chezy coefficient

ChannelLength

scalar, spatial

[m] > 0

ChannelBottomWidth

scalar, spatial

[m] >= 0

ChannelDepth

scalar, spatial

[m] > 0

ChannelForm

scalar, spatial

[-] >= 0

FloodPlainWidth

scalar, spatial

[m] >= ChannelBottomWidth + ChannelDepth*ChannelForm

TimeStepInSeconds

scalar, non-spatial

[sec] > 0

NrOfTimeSlices

scalar, non-spatial

[-] > 0

Structures

boolean, spatial

[-] False/True values expected on defined Ldd cells

StructureA

scalar, spatial

[-] values expected where Structures is True

StructureB

scalar, spatial

[-] values expected where Structures is True

StructureCrestLevel

scalar, spatial

[-] values expected where Structures is True

ResultQ

scalar, spatial

[m3/timestep] Dynamic wave flow along the defined LDD

ResultH

scalar, spatial

[m] New water level Dynamic wave flow along the defined LDD. The next timestep, this resultH can be used as Hin.

../../_images/DynamicWaveChannel.png

Definition of the channel arguments

Global options:

The algortithm is influenced by the options --manning (default) or --chezy, to select the dynamic flow equation (see below for these equations).

Operation

For an extended discussion of the Dynamic Wave equations is referred to textbooks on hydraulic modelling and hydrology (Chow and Chanson). The most important equation used is to calculate for each iteration step the dynamic flow as a function of water level and slope in water surface (Manning equation):

\[ResultQ = (Aact * \sqrt{Sf} * R^{2/3}) / ManningCoeff\]

or, in case of the Chezy equation:

\[ResultQ = ChezyCoeff * Aact * \sqrt{Sf} * \sqrt{R}\]

In which Aact is the wetted surface, calculated from the ChannelBottomWidth, ChannelForm and Hin (water level), R is the wet perimeter, calculated from ChannelBottomWidth, ChannelForm and Hin, and Sf is the slope in water surface, so the waterlevel upstream minus waterlevel downstream cell.

The volume of water in each cell is updated for the outflow of that cell and the inflow from above cells. Based on the new volume, a new water level H is calculated.

This set of equations is evaluated through the entire channel network, for iteration steps which are equal to TimeStepsInSeconds/NrOfTimeSlices.

The approach taken for structures is a generic approach, which defines outflow from or overflow over the structure using the formula

\[\begin{split}Qstructure = \begin{cases} StructureA*((Hin-StructureCrestLevel)**StructureB) \text{ if $Hin > $StructureCrestLevel},\\ 0 \text{ otherwise}. \end{cases}\end{split}\]

Boundary conditions

Boundary conditions for the dynamic wave should be modelled as fixed water levels. In the situation of a fixed water level, within the dynamic section the points with fixed water levels should overwrite the results of the water level before using them in the next timestep.

Example:

initial
  FixedWaterLevel = Level.map;
  FixedPoints = Points.map;
  Hin = InitialWaterLevel;
dynamic
  …
  DynWaveQ, DynWaveH = dynamicwaveq,dynamicwaveh(LDD,Qin, Hin, ………);
  Hin = if(FixedPoints then FixedWaterLevel else DynWaveH);
  …